Journal of Applied Mathematics

Quenching Time Optimal Control for Some Ordinary Differential Equations

Ping Lin

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

This paper concerns time optimal control problems of three different ordinary differential equations in 2 . Corresponding to certain initial data and controls, the solutions of the systems quench at finite time. The goal to control the systems is to minimize the quenching time. The purpose of this study is to obtain the existence and the Pontryagin maximum principle of optimal controls. The methods used in this paper adapt to more general and complex ordinary differential control systems with quenching property. We also wish that our results could be extended to the same issue for parabolic equations.

Article information

Source
J. Appl. Math., Volume 2014 (2014), Article ID 127809, 13 pages.

Dates
First available in Project Euclid: 2 March 2015

Permanent link to this document
https://projecteuclid.org/euclid.jam/1425305676

Digital Object Identifier
doi:10.1155/2014/127809

Mathematical Reviews number (MathSciNet)
MR3198357

Citation

Lin, Ping. Quenching Time Optimal Control for Some Ordinary Differential Equations. J. Appl. Math. 2014 (2014), Article ID 127809, 13 pages. doi:10.1155/2014/127809. https://projecteuclid.org/euclid.jam/1425305676


Export citation

References

  • H. Kawarada, “On solutions of initial-boundary problem for ${u}_{t}={u}_{xx}+1/(1-u)$,” Publications of the Research Institute for Mathematical Sciences, vol. 10, no. 3, pp. 729–736, 1975.
  • C. Y. Chan and H. G. Kaper, “Quenching for semilinear singular parabolic problems,” SIAM Journal on Mathematical Analysis, vol. 20, no. 3, pp. 558–566, 1989.
  • V. Barbu, Analysis and Control of Nonlinear Infinite-Dimensional Systems, vol. 190, Academic Press, Boston, Mass, USA, 1993.
  • H. O. Fattorini, Infinite Dimensional Linear Control Systems. The Time Optimal and Norm Optimal Problems, vol. 201, Elsevier Science, Amsterdam, The Netherlands, 2005.
  • X. J. Li and J. M. Yong, Optimal Control Theory for Infinite-Dimensional Systems, Birkhäuser, Boston, Mass, USA, 1995.
  • S. Luan, H. Gao, and X. Li, “Optimal control problem for an elliptic equation which has exactly two solutions,” Optimal Control Applications & Methods, vol. 32, no. 6, pp. 734–747, 2011.
  • G. Zheng and B. Ma, “A time optimal control problem of some linear switching controlled ordinary differential equations,” Advances in Difference Equations, vol. 2012, article 52, 7 pages, 2012.
  • P. Lin and G. Wang, “Blowup time optimal control for ordinary differential equations,” SIAM Journal on Control and Optimization, vol. 49, no. 1, pp. 73–105, 2011.
  • P. Lin, “Quenching time optimal control for some ordinary differential equations,” http://arxiv.org/abs/1209.0784. In press. \endinput